We all reason about what we ought to do, what should be, and what is permissible, but neither Standard Deontic Logic (SDL) nor its more recent variants adequately represent the principles of our deontic reasoning. In this groundbreaking new work, author James Forrester first explores the shortcomings of standard deontic systems, and concludes that we need a new type of deontic logic; in the second part of the book, he presents a new deontic logic and semantics that fit our deontic reasoning better than standard systems. Finally, in a third section, Forrester sketches some original implications of his new deontic logic for practical reasoning. This book will be of interest to all philosophers, especially those with an interest in questions of moral and practical reasoning.

A new direction in philosophy
Between 1920 and 1940 logical empiricism reset the direction of philosophy of science and much of the rest of Anglo-American philosophy. It began as a relatively organized movement centered on the Vienna Circle, and like-minded philosophers elsewhere, especially in Berlin. As Europe drifted into the Nazi era, several important figures, especially Carnap and Neurath, also found common ground in their liberal politics and radical social agenda. Together, the logical empiricists set out to reform traditional philosophy with a new set of doctrines more firmly grounded in logic and science.
Criticism and decline
Because of Nazi persecution, most of the European adherents of logical empiricism moved to the United States in the late 1930s. During the 1940s, many of their most cherished tenets became targets of criticism from outsiders as well as from within their own ranks. Philosophers of science in the late 1950s and 1960s rejected logical empiricism and, starting in the 1970s, presented such alternative programs such as scientific realism with evolutionary epistemology.
A resurgence of interest
During the early 1980s, philosophers and historians of philosophy began to study logical empiricism as an important movement. Unlike their predecessors in the 1960s-for whom the debate over logical empiricism now seems to have been largely motivated by professional politics-these philosopher no longer have to take positions for or against logical empiricism. The result has been a more balanced view of that movement, its achievements, its failures, and its influence.
Hard-to-find core writings now available
This collection makes available aselection of the most influential and representative writings of the logical empiricists, important contemporary criticisms of their doctrines, their responses, as well as the recent reappraisals. Introductions to each volume examine the articles in historical context and provide important background information that is vital to a full understanding of the issues discussed. They outline prevalent trends, identifying leading figures and summarize their positions and reasoning, as well as those of opposing thinkers.

A new direction in philosophy
Between 1920 and 1940 logical empiricism reset the direction of philosophy of science and much of the rest of Anglo-American philosophy. It began as a relatively organized movement centered on the Vienna Circle, and like-minded philosophers elsewhere, especially in Berlin. As Europe drifted into the Nazi era, several important figures, especially Carnap and Neurath, also found common ground in their liberal politics and radical social agenda. Together, the logical empiricists set out to reform traditional philosophy with a new set of doctrines more firmly grounded in logic and science.
Criticism and decline
Because of Nazi persecution, most of the European adherents of logical empiricism moved to the United States in the late 1930s. During the 1940s, many of their most cherished tenets became targets of criticism from outsiders as well as from within their own ranks. Philosophers of science in the late 1950s and 1960s rejected logical empiricism and, starting in the 1970s, presented such alternative programs such as scientific realism with evolutionary epistemology.
A resurgence of interest
During the early 1980s, philosophers and historians of philosophy began to study logical empiricism as an important movement. Unlike their predecessors in the 1960s-for whom the debate over logical empiricism now seems to have been largely motivated by professional politics-these philosopher no longer have to take positions for or against logical empiricism. The result has been a more balanced view of that movement, its achievements, its failures, and its influence.
Hard-to-find core writings now available
This collection makes available aselection of the most influential and representative writings of the logical empiricists, important contemporary criticisms of their doctrines, their responses, as well as the recent reappraisals. Introductions to each volume examine the articles in historical context and provide importantbackground information that is vital to a full understanding of the issues discussed. They outline prevalent trends, identifying leading figures and summarize their positions and reasoning, as well as those of opposing thinkers.

A new direction in philosophy
Between 1920 and 1940 logical empiricism reset the direction of philosophy of science and much of the rest of Anglo-American philosophy. It began as a relatively organized movement centered on the Vienna Circle, and like-minded philosophers elsewhere, especially in Berlin. As Europe drifted into the Nazi era, several important figures, especially Carnap and Neurath, also found common ground in their liberal politics and radical social agenda. Together, the logical empiricists set out to reform traditional philosophy with a new set of doctrines more firmly grounded in logic and science.
Criticism and decline
Because of Nazi persecution, most of the European adherents of logical empiricism moved to the United States in the late 1930s. During the 1940s, many of their most cherished tenets became targets of criticism from outsiders as well as from within their own ranks. Philosophers of science in the late 1950s and 1960s rejected logical empiricism and, starting in the 1970s, presented such alternative programs such as scientific realism with evolutionary epistemology.
A resurgence of interest
During the early 1980s, philosophers and historians of philosophy began to study logical empiricism as an important movement. Unlike their predecessors in the 1960s-for whom the debate over logical empiricism now seems to have been largely motivated by professional politics-these philosopher no longer have to take positions for or against logical empiricism. The result has been a more balanced view of that movement, its achievements, its failures, and its influence.
Hard-to-find core writings now available
This collection makes available aselection of the most influential and representative writings of the logical empiricists, important contemporary criticisms of their doctrines, their responses, as well as the recent reappraisals. Introductions to each volume examine the articles in historical context and provide importantbackground information that is vital to a full understanding of the issues discussed. They outline prevalent trends, identifying leading figures and summarize their positions and reasoning, as well as those of opposing thinkers.

A new direction in philosophy
Between 1920 and 1940 logical empiricism reset the direction of philosophy of science and much of the rest of Anglo-American philosophy. It began as a relatively organized movement centered on the Vienna Circle, and like-minded philosophers elsewhere, especially in Berlin. As Europe drifted into the Nazi era, several important figures, especially Carnap and Neurath, also found common ground in their liberal politics and radical social agenda. Together, the logical empiricists set out to reform traditional philosophy with a new set of doctrines more firmly grounded in logic and science.
Criticism and decline
Because of Nazi persecution, most of the European adherents of logical empiricism moved to the United States in the late 1930s. During the 1940s, many of their most cherished tenets became targets of criticism from outsiders as well as from within their own ranks. Philosophers of science in the late 1950s and 1960s rejected logical empiricism and, starting in the 1970s, presented such alternative programs such as scientific realism with evolutionary epistemology.
A resurgence of interest
During the early 1980s, philosophers and historians of philosophy began to study logical empiricism as an important movement. Unlike their predecessors in the 1960s-for whom the debate over logical empiricism now seems to have been largely motivated by professional politics-these philosopher no longer have to take positions for or against logical empiricism. The result has been a more balanced view of that movement, its achievements, its failures, and its influence.
Hard-to-find core writings now available
This collection makes available aselection of the most influential and representative writings of the logical empiricists, important contemporary criticisms of their doctrines, their responses, as well as the recent reappraisals. Introductions to each volume examine the articles in historical context and provide importantbackground information that is vital to a full understanding of the issues discussed. They outline prevalent trends, identifying leading figures and summarize their positions and reasoning, as well as those of opposing thinkers.

Contents:
Preface 1. Introduction 2. Argument and Evidence 3. Context, Convention and Communication 4. An informal Analysis of Arguments 5. Patterns of Reasoning 6. Establishing Validity 7. Critical Analysis in Practice 8.Assumptions 9. Evidence as Ground Belief 10. What Counts as Evidence? 11. Presenting and Summarising Evidence 12. Furthering Knowledge 13. Probability and Uncertainty 14. Probability Theory applied 15. Estimation and Reliability 16. Testing Hypotheses; Appendices; Glossery; References

Free logic is an important field of philosophical logic that first appeared in the 1950s. J. Karel Lambert was one of its founders and coined the term. The essays in this collection (written over a period of 40 years) explore the philosophical foundations of free logic and its application to areas as diverse as the philosophy of religion and computer science. This collection brings an important body of work to the attention of a new generation of professional philosophers, computer scientists and mathematicians.

This book aims to lay bare the logical foundations of tractable reasoning. It draws on Marvin Minsky's seminal work on frames, which has been highly influential in computer science and, to a lesser extent, in cognitive science. Only very few people have explored ideas about frames in logic, which is why the investigation in this book breaks new ground. The apparent intractability of dynamic, inferential reasoning is an unsolved problem in both cognitive science and logic-oriented artificial intelligence. By means of a logical investigation of frames and frame concepts, Andreas devises a novel logic of tractable reasoning, called frame logic. Moreover, he devises a novel belief revision scheme, which is tractable for frame logic. These tractability results shed new light on our logical and cognitive means to carry out dynamic, inferential reasoning. Modularity remains central for tractability, and so the author sets forth a logical variant of the massive modularity hypothesis in cognitive science. This book conducts a sustained and detailed examination of the structure of tractable and intelligible reasoning in cognitive science and artificial intelligence. Working from the perspective of formal epistemology and cognitive science, Andreas uses structuralist notions from Bourbaki and Sneed to provide new foundational analyses of frames, object-oriented programming, belief revision, and truth maintenance. Andreas then builds on these analyses to construct a novel logic of tractable reasoning he calls frame logic, together with a novel belief revision scheme that is tractable for frame logic. Put together, these logical analyses and tractability results provide new understandings of dynamic and inferential reasoning. Jon Doyle, North Carolina State University

This volume is a collection of essays in honour of Professor Mohammad Ardeshir. It examines topics which, in one way or another, are connected to the various aspects of his multidisciplinary research interests. Based on this criterion, the book is divided into three general categories. The first category includes papers on non-classical logics, including intuitionistic logic, constructive logic, basic logic, and substructural logic. The second category is made up of papers discussing issues in the contemporary philosophy of mathematics and logic. The third category contains papers on Avicenna's logic and philosophy. Mohammad Ardeshir is a full professor of mathematical logic at the Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran, where he has taught generations of students for around a quarter century. Mohammad Ardeshir is known in the first place for his prominent works in basic logic and constructive mathematics. His areas of interest are however much broader and include topics in intuitionistic philosophy of mathematics and Arabic philosophy of logic and mathematics. In addition to numerous research articles in leading international journals, Ardeshir is the author of a highly praised Persian textbook in mathematical logic. Partly through his writings and translations, the school of mathematical intuitionism was introduced to the Iranian academic community.

In the past 15 years a host of critical thinking books have appeared that teach students to find flaws in the arguments of others by learning to detect a number of informal fallacies. This book is not in that tradition. The authors of this book believe that while students learn to become vicious critics, they still continue to make the very mistakes they criticize in others. Thus, this book has adopted the approach of teaching the construction of good arguments first and then introducing criticism as a secondary skill. Moreover, the emphasis of the book is not on learning to name fallacies, but on being able to identify weaknesses in an argument so as to be able to construct an effective critique of that argument. The book is accompanied by a workbook featuring a wealth of examples to help students acquire the material.

This textbook offers a detailed introduction to the methodology and applications of sequent calculi in propositional logic. Unlike other texts concerned with proof theory, emphasis is placed on illustrating how to use sequent calculi to prove a wide range of metatheoretical results. The presentation is elementary and self-contained, with all technical details both formally stated and also informally explained. Numerous proofs are worked through to demonstrate methods of proving important results, such as the cut-elimination theorem, completeness, decidability, and interpolation. Other proofs are presented with portions left as exercises for readers, allowing them to practice techniques of sequent calculus. After a brief introduction to classical propositional logic, the text explores three variants of sequent calculus and their features and applications. The remaining chapters then show how sequent calculi can be extended, modified, and applied to non-classical logics, including modal, intuitionistic, substructural, and many-valued logics. Sequents and Trees is suitable for graduate and advanced undergraduate students in logic taking courses on proof theory and its application to non-classical logics. It will also be of interest to researchers in computer science and philosophers.

For Plato, philosophy depends on, or is perhaps even identical with, dialectic. Few will dispute this claim, but there is little agreement as to what Platonic dialectic is. According to a now prevailing view it is a method for inquiry the conception of which changed so radically for Plato that it "had a strong tendency ... to mean 'the ideal method', whatever that may be" (Richard Robinson). Most studies of Platonic dialectic accordingly focus on only one aspect of this method that allegedly characterizes one specific period in Plato's development. This volume offers fresh perspectives on Platonic dialectic. Its 13 chapters present a comprehensive picture of this crucial aspect of Plato's philosophy and seek to clarify what Plato takes to be proper dialectical procedures. They examine the ways in which these procedures are related to each other and other aspects of his philosophy, such as ethics, psychology, and metaphysics. Collectively, the chapters challenge the now prevailing understanding of Plato's ideal of method. New Perspectives on Platonic Dialectic will appeal to scholars and advanced students interested in Plato, ancient philosophy, philosophical method, and the history of logic.

This edited book focuses on non-classical logics and their applications, highlighting the rapid advances and the new perspectives that are emerging in this area. Non-classical logics are logical formalisms that violate or go beyond classical logic laws, and their specific features make them particularly suited to describing and reason about aspects of social interaction. The richness and diversity of non-classical logics mean that this area is a natural catalyst for ideas and insights from many different fields, from information theory to game theory and business science. This volume is the post-proceedings of the 8th International Conference on Logic and Cognition, held at Sun Yat-Sen University Institute of Logic and Cognition (ILC) in Guangzhou, China in December 2016. The conference series started in 2001, and is organized by the ILC, often in collaboration with various international research groups. This eighth installment was jointly organized by ILC and Alessandra Palmigiano's Applied Logic research group. The conference series aims to foster the development of effective logical tools to study social behavior from a philosophical, cognitive and formal perspective in order to challenge the field of logic in ways that open up new and exciting research directions. Chapter "The Category of Node-and-Choice Forms, with Subcategories for Choice-Sequence Forms and Choice-Set Forms" of this book is available open access under a CC BY 4.0 license at link.springer.com

The purpose of this book is to present unpublished papers at the cutting edge of research on dialetheism and to reflect recent work on the applications of the theory. It includes contributions from some of the most respected scholars in the field, as well as from young, up-and-coming philosophers working on dialetheism. Moving from the fringes of philosophy to become a main player in debates concerning truth and the logical paradoxes, dialetheism has thrived since the publication of Graham Priest's In Contradiction, and several of the papers find their roots in a conference on dialetheism held in Glasgow to mark the 25th anniversary of Priest's book. The content presented here demonstrates the considerable body of work produced in this field in recent years. With a broad focus, this book also addresses the applications of dialetheism outside the more familiar area of the logical paradoxes, and includes pieces discussing the application of dialetheism in metaphysics, philosophy of language, and philosophy of mind.

This volume presents different conceptions of logic and mathematics and discuss their philosophical foundations and consequences. This concerns first of all topics of Wittgenstein's ideas on logic and mathematics; questions about the structural complexity of propositions; the more recent debate about Neo-Logicism and Neo-Fregeanism; the comparison and translatability of different logics; the foundations of mathematics: intuitionism, mathematical realism, and formalism. The contributing authors are Matthias Baaz, Francesco Berto, Jean-Yves Beziau, Elena Dragalina-Chernya, Gunther Eder, Susan Edwards-McKie, Oliver Feldmann, Juliet Floyd, Norbert Gratzl, Richard Heinrich, Janusz Kaczmarek, Wolfgang Kienzler, Timm Lampert, Itala Maria Loffredo D'Ottaviano, Paolo Mancosu, Matthieu Marion, Felix Muhlhoelzer, Charles Parsons, Edi Pavlovic, Christoph Pfisterer, Michael Potter, Richard Raatzsch, Esther Ramharter, Stefan Riegelnik, Gabriel Sandu, Georg Schiemer, Gerhard Schurz, Dana Scott, Stewart Shapiro, Karl Sigmund, William W. Tait, Mark van Atten, Maria van der Schaar, Vladimir Vasyukov, Jan von Plato, Jan Wolenski and Richard Zach.

Fred Stoutland was a major figure in the philosophy of action and philosophy of language. This collection brings together essays on truth, language, action and mind and thus provides an important summary of many key themes in Stoutland's own work, as well as offering valuable perspectives on key issues in contemporary philosophy.

Many systems of logic diagrams have been offered both historically and more recently. Each of them has clear limitations. An original alternative system is offered here. It is simpler, more natural, and more expressively and inferentially powerful. It can be used to analyze not only syllogisms but arguments involving relational terms and unanalyzed statement terms.

What do the rules of logic say about the meanings of the symbols they govern? In this book, James W. Garson examines the inferential behaviour of logical connectives (such as 'and', 'or', 'not' and 'if ... then'), whose behaviour is defined by strict rules, and proves definitive results concerning exactly what those rules express about connective truth conditions. He explores the ways in which, depending on circumstances, a system of rules may provide no interpretation of a connective at all, or the interpretation we ordinarily expect for it, or an unfamiliar or novel interpretation. He also shows how the novel interpretations thus generated may be used to help analyse philosophical problems such as vagueness and the open future. His book will be valuable for graduates and specialists in logic, philosophy of logic, and philosophy of language.

This book presents the research achievements of Jin Yuelin, the first logician and a prominent philosopher in China, who founded a new philosophical system combining elements from Western and Chinese philosophical traditions, especially the concept of Tao. It consists of three sections: the first section interprets Jin's studies on Chinese philosophy, Russell's ideology and other general discussions in the field; section 2 includes Jin's studies on logic, which made him the founding father of modern logic in China; and section 3 presents Jin's ideas on politics, including his studies on Thomas Hill Green.

Truth Be Told explains how truth and falsity result from relations that sentences have to the contexts in which they occur and the circumstances at which they are evaluated. It offers a precise conception of truth and a clear diagnosis of the Liar and Grelling paradoxes. Currently, semantic theory employs generalized quantifiers as the extensions of noun phrases in explanations of the composition of truth-values. Generalized quantifiers are direct descendants of the second-level functions to truth-values that Gottlob Frege considered to be the referents of his unrestricted quantifiers. During the past fifty years, Frege's original quantifier referents have been revised and generalized with the result that now every noun phrase, of any type, has a generalized quantifier as its extension. This evolution of noun-phrase extensions from Frege's referents has retained two of the original theory's flaws. First, generalized quantifiers inherit a troublesome intrusion of predicate extensions. Second, the senses of names and deictic terms are still not identified, with the result that their extensions are not sharply distinguished from their referents. Truth Be Told frees semantic theory from these Fregean flaws. Its theory of sense, quantity, and extension yields an intuitive composition of sentence truth-values and secures an accurate understanding of truth. Its final chapter applies the theory in a diagnosis of the Liar and Grelling paradoxes that is immune to the notorious revenge paradoxes. Truth Be Told can be used for courses in philosophy of language, semantics, and the foundations of logic.

I have been thinking about the philosophical issue of truth for more than two decades. It is one of several fascinating philosophical issues that motivated me to change my primary re ective interest to philosophy after receiving BS in mathem- ics in 1982. Some serious academic work in this connection started around the late eighties when I translated into Chinese a dozen of Donald Davidson's representative essays on truth and meaning and when I assumed translator for Adam Morton who gave a series of lectures on the issue in Beijing (1988), which was co-sponsored by my then institution (Institute of Philosophy, Chinese Academy of Social Science). I have loved the issue both for its own sake (as one speci c major issue in the phil- ophy of language and metaphysics) and for the sake of its signi cant involvement in many philosophical issues in different subjects of philosophy. Having been attracted to the analytic approach, I was then interested in looking at the issue both from the points of view of classical Chinese philosophy and Marxist philosophy, two major styles or frameworks of doing philosophy during that time in China, and from the point of view of contemporary analytic philosophy, which was then less recognized in the Chinese philosophical circle.

This book presents the state of the art in the fields of formal logic pioneered by Graham Priest. It includes advanced technical work on the model and proof theories of paraconsistent logic, in contributions from top scholars in the field. Graham Priest's research has had a considerable influence on the field of philosophical logic, especially with respect to the themes of dialetheism-the thesis that there exist true but inconsistent sentences-and paraconsistency-an account of deduction in which contradictory premises do not entail the truth of arbitrary sentences. Priest's work has regularly challenged researchers to reappraise many assumptions about rationality, ontology, and truth. This book collects original research by some of the most esteemed scholars working in philosophical logic, whose contributions explore and appraise Priest's work on logical approaches to problems in philosophy, linguistics, computation, and mathematics. They provide fresh analyses, critiques, and applications of Priest's work and attest to its continued relevance and topicality. The book also includes Priest's responses to the contributors, providing a further layer to the development of these themes .

This volume comprises a selection of contributions to the theorizing about argumentation that have been presented at the 9th conference of the International Society for the Study of Argumentation (ISSA), held in Amsterdam in July 2018. The chapters included provide a general theoretical perspective on central topics in argumentation theory, such as argument schemes and the fallacies. Some contributions concentrate on the treatment of the concept of conductive argument. Other contributions are dedicated to specific issues such as the justification of questions, the occurrence of mining relations, the role of exclamatives, argumentative abduction, eudaimonistic argumentation and a typology of logical ways to counter an argument. In a number of cases the theoretical problems addressed are related to a specific type of context, such as the burden of proof in philosophical argumentation, the charge of committing a genetic fallacy in strategic manoeuvring in philosophy, the necessity of community argument, and connection adequacy for arguments with institutional warrants. The volume offers a great deal of diversity in its breadth of coverage of argumentation theory and wide geographic representation from North and South America to Europe and China.

The conditional, if...then, is probably the most important term in natural language and forms the core of systems of logic and mental representation. It occurs in all human languages and allows people to express their knowledge of the causal or law-like structure of the world and of others' behaviour, e.g., if you turn the key the car starts, if John walks the dog he stops for a pint of beer; to make promises, e.g., if you cook tonight, I'll wash up all week; to regulate behaviour, e.g., if you are drinking beer, you must be over 18 years of age; to suggest what would have happened had things been different, e.g., if the match had been dry it would have lit, among many other possible uses. The way in which the conditional is modelled also determines the core of most logical systems. Unsurprisingly, it is also the most researched expression in the psychology of human reasoning.
Cognition and Conditionals is the first volume for over 20 years (On Conditionals, 1986, CUP) that brings together recent developments in the cognitive science and psychology of conditional reasoning. Over the last 10 to 15 years, research on conditionals has come to dominate the psychology of reasoning providing a rich seam of results that have created new theoretical possibilities. This book shows how these developments have led researchers to view people's conditional reasoning behaviour more as succesful probabilistic reasoning rather than as errorful logical reasoning. It shows how the multifarious, and apparently competing, theoretical positions developed over the last 50 years in this area - mental logics, mental models, heuristic approaches, dual process theory, and probabilistic approaches-have responded to these insights. Its organisation reflects the view that an integrative approach is emerging that may need to exploit aspects of all these theoretical positions to explain the rich and complex phenomenon of reasoning with conditionals. It includes an introductory chapter relating the development of the psychology of reasoning to developments in the logic and semantics of the conditional. It also includes chapters by many of the leading figures in this field.
Cognition and Conditionals will be a valuable resource for cognitive scientists, psychologists and philosophers interested how people actually reason with conditionals.

This book bridges the gaps between logic, mathematics and computer science by delving into the theory of well-quasi orders, also known as wqos. This highly active branch of combinatorics is deeply rooted in and between many fields of mathematics and logic, including proof theory, commutative algebra, braid groups, graph theory, analytic combinatorics, theory of relations, reverse mathematics and subrecursive hierarchies. As a unifying concept for slick finiteness or termination proofs, wqos have been rediscovered in diverse contexts, and proven to be extremely useful in computer science. The book introduces readers to the many facets of, and recent developments in, wqos through chapters contributed by scholars from various fields. As such, it offers a valuable asset for logicians, mathematicians and computer scientists, as well as scholars and students.